Demographics and Macroeconomics - Part 1 (Wonkish)
Blog post series, like the vuvuzela, is the new bacon; it works with everything and with John Hempton’s recent excellent series on the economics of default in the Eurozone and Edward’s recent postings on AFOE in which he pulls out some of our old paper abstracts has inspired me to a series in which I try to pin point exactly how demographics and macroeconomics interact and where I believe we need more focus and work.
When it comes to the overall link between demographics and macroeconomics we already have a number of core workhorse models in the form of the life cycle and life course framework where the former deals with consumption and savings decisions as a function of age and the latter deals, broadly, with life time events and their individual and aggregate importance on economic dynamics. The adequate impact on the macro economy from the dynamics of demographics must then be developed as a function of the attempt to do two things; firstly, to continuously develop the life cycle and life course theories themselves and secondly to seek out new ways to apply life cycle and life course theory to existing macroeconomic problems and themes.
In the first series, I will begin with the latter. Overall, I will highlight 6 areas where demographics enter macroeconomic theory and research as an important variable and I will try to offer my view on where to progress further. I will begin with two classics in the form of growth theory and open economy dynamics.
Firstly, I need to say that I am not an expert on growth theory and this represents somewhat of a problem since growth theory although somewhat out of vogue at the moment has grown to become an extremely diverse field with a wide number of different schools and discourses. For the purpose here it will suffice to note that most economists today still use some form of the classic production function framework which has its roots in the work by Charles Cobb and Paul Douglas in 1928 and was popularized in 1958 by Solow’s famous article. This is what it looks like;
Where Y is output, K is physical capital, A is the illusive residual or more specifically technology/production function, L is the size of the labour force and H is a measure of human capital. Now, I certainly won’t do any math at this point and it is important to note that the functional form may take many exotic forms (which are not necessarily Cobb-Douglas), but just to give you one example the following is a Cobb-Douglas production function which incorporates human capital as above (here with constant returns to scale);
The key point I want to emphasize here is simply that we have output as a function of some input and that we would like to account for and explain the dynamics and behaviour of this input. How might we imbue this model with reasonable characteristics that reflect demographic dynamics? As it turns out, we already have some pretty solid frameworks to deal with this questions and we can see this by looking at the inputs one at a time.
The evolution of capital (K) – In most traditional models the evolution of capital is simply expressed as the fraction of income save minus any depreciation of the capital stock in the last period and here of course we have several workhorse models to show demographic dynamics that are all wrapped up in the form of the life cycle hypothesis of savings and consumption. Usually and since most of these models are constructed on the basis of Walrasian microfoundations, we have some form of intertemporal optimization problem ticking away in the background which assumes an OLG (overlapping generations) form. The classic model here is the Diamond model who is based on Diamond (1965) which is the father of all OLG models, but over time a plethora of different OLG models have been developed with differing degree of analytical complexity.
The basic problem here though remains the concept of the steady state which means that we must construct model such as to allow the change of capital through time (or its derivative with time) to be 0 in the long run. Please note here that this condition is not imposed on the basis of empirical behaviour but on the basis of (mathematical) analytical tractability. So, apart from the uncertainty surrounding exactly what this ”long run” is it also locks in the analysis and assumes away a large part of the important aspects of even basic life cycle behavior. Specifically, the idea that once reaching a steady state any change in the savings/consumption rate will one have transitory effect and that the economy will automatically (and always) converge to the same growth rate/state as before is a problem. Essentially, the whole idea of a steady state whether be it in the form of an exogenous or endogenous growth theory framework is a huge problem since it is evident that such a thing does not exist. And even if we could establish over a very long run horizon that such an average/constant path is a good approximation we would be ironing out all the interesting and important questions in the process.
The evolution of human capital (H) – The adoption of human capital into the growth theory framework is famously due to a paper by Mankiw, Romer and Weil in 1992 in which human capital is proxied by rates of schooling and thus the perspective becomes one of the quality of human capital and to the extent that the formation of human capital also includes the evolution of the population (or perhaps working age population) we can say that this is a direct way in which demographics enter the framework. Again, we might simply ask here; to what extent does the aggregate quality of human capital in an economy depend on the age structure of its population and here I am not only talking about the level of education but much more broadly about the idea of innovative capacity as a function of population structure.
The evolution of technology (A) – Technology and productivity are famously assumed exogenous in the Neo-Classical tradition while New Growth theory as it was developed in the 1980s and 1990s emphasised the need to specifically account for the evolution of technology. Today, I would venture the claim that there is a consensus that productivity and technology is a function of what we could call, broadly, institutional quality which encompass almost anything imaginable from basic property rights to the level of entrepreneurship. Indeed, a large part of research is still devoted to pinning down exactly which determinants that are most important here both across countries and through time. Now, I would argue that, in the context of standard growth theory, this is where the scope for the study of the effect of population dynamics is largest. Thus I don’t think it is unreasonable to expect the level and evolution of productivity growth and technological development to be a function of the current population structure but also its velocity which is a function of e.g. migration (new inputs?), future working age size etc. Also, this is also where human capital and the evolution of technology is joined at the hip through the idea of innovative capacity and readiness.
As you might have inferred from the exposition above, I have some difficulties with growth theory. I can admire the framework for its internal logic and I can see why it is an important part of a macroeconomist’s toolkit, but I also think that growth theory (as I describe it above) has outlived itself. In this sense, most of the questions that we have as economists when it comes to the evolution of growth and welfare of our economies both individually and through their interaction is not addressed by growth theory. Especially the effect of an ongoing and ruthless process of ageing is completely impossible to analyse in the standard framework. Naturally, I am also being a bit unfair here since the kind of growth theory I am describing above is also too simple to give adequate credit to where the field is today. For example in relation to demographics, I am grossly overlooking important strides in the development of OLG models which have been perfected continuously so that we today have a very large battery of very complex models. But also more generally, growth theory is being used today to produce a lot of useful research. As I say, it remains a key tool in our toolbox.
Yet, the basic growth theoretical setup remains flawed in key a number of un-salvagable ways. Concretely, specifying a production function and specifying the underlying inputs as differential equations through whose solution we reach a steady state equilibrium is not, in my opinion, the way to go. Thus and in an intuitive sense I feel much more at home, for example, in the company of evolutionary growth theorists  whose argument and methodology is more agile. In summary then and as I try my utmost not to become a hostage of the notion of a steady state I will simply make the following observations in the context of what we macroeconomists consider the main inputs to growth where the ”age” is simply an unspecified collection/function of variables that pertains to fertility, age structure, mortality etc (and of course a whole slew of other factors, but for the sake of argument let us keep it monocausal here).
Where age in the context of the capital stock relates to the size and evolution of the capital stock as well as savings and investment dynamics, in the context of human capital it may be argued to enter directly, but may also affect the quality of human capital. Finally, I think that the impact of demographics on innovation and especially the idea of velocity of innovation and innovative capacity represents an area which is not well understood. In general though and short of letting some variant of demographics enter directly, I think an important research program would be to examine the effect from demographics on the inputs to growth which we traditionally operate with. Especially, the process unprecedented process of ageing is a completely new phenomenon here in the context of traditional growth theoretical analysis.
Open Economy Dynamics
An enduring feature of macroeconomics is that the entities we study are not black boxes but interdependent entities who interact in very complex ways in the global economy. This statement was true 40-50 years ago and today it is almost a cliché. In fact, for non-macroeconomists it must seem very strange that we still distinguish so strongly between closed and open economy analysis as the use of studying the former must surely be almost nill. I would agree with this statement but simply note that important things do actually happen when we go from a closed to an open economy and the way this transition is operationalised is important in itself.
Now, I could write a lot about this (in fact, I have penned a whole thesis about it), but I will only cover the essentials. What you need to know upfront are two things. The first is that the economic theory used to handle the effect of age structure/demographics on open economy dynamics is again the life cycle framework and, in most cases, we still have a OLG representative agent model taking care of the microfoundations. Secondly, it is important to be aware of the concrete specifics of the transition from a closed to an open economy. Luckily, this can be handled by some very simple algebra from macroeconomics 1-0-1.
The whole point is to find an expression for savings, so for the closed economy we have;
By definition every unit of output has to equal a unit of income, and national income in any given period can either be saved or consumed. This means that national income can either be put aside for saving or consumed through government (G) or private consumption (C). In this way, we define national saving in any given period as;
This is a fundamental result in basic macroeconomics and what is equally fundamental is why this changes in one key aspect when we move into an open economy setting. We then have;
With (x-m) equal to the trade balance and by doing the same exercise above we get;
In this context and remembering that the life cycle hypothesis tries to map consumption and saving as a function of age, the transition from a closed to an open economy becomes crucial in order to see how demographics may affect open economy dynamics. As such, allow me to quote the following passage of my thesis which I find myself coming back to when thinking about this topic;
The best way to think about this  is to imagine that savings and investment are in a race governed and controlled, as it were, by the transition in age structure that occurs as a result of the demographic transition. Initially, as the transition sets in with a decline in mortality and where fertility only follows with a lag, investment demand outruns the supply of savings and the economy is running an external deficit. Steadily however, the supply of saving catches up with investment demand which itself begins to decline and thus the external balance moves into a surplus. Finally, the pace of savings accumulation is replaced by outright decumulation (dissaving) and the external balance moves into deficit as savings decline faster than domestic investment demand
This is stylized of course, but especially the idea of the race between savings and investment is a very helpful metaphor. Consider then a closed economy; in such a setting there can be no race as described above since savings and investment will be tied together at all points in time, but in an open economy savings and investment dynamics are exactly what provokes relations between economies and more specifically, the fact that the economies have different preferences for savings and investment at different points in time. This gives a very strong foundation for thinking about how demographics affect open economy dynamics.
Concretely, and in order to tie the argument up on the underlying theory capital flows occur precisely because economies have different intertemporal preferences for consumption and saving and since this intertemporal preference itself is a function of age (through the life cycle/OLG framework) demographics become a driving force for international capital flows.
This as it were is also where the fun begins since exactly how this process should be understood both from the point of view of the individual economy, but also in a global context remains, for all intent and purposes, an unresolved question. Surely, we have studies that use basic life cycle frameworks to simulate capital flows between economies and they do have some intuitive appeal and explanatory power, but they are hampered by, in my opinion, by an inadequate understanding of the life cycle thesis and how exactly it manifests itself. As I noted in the beginning, part of all this also requires a continuous development of the life cycle hypothesis itself and here this becomes important. Personally, I have cast my eyes on two areas of research where I believe that the influence of demographics on open economy dynamics is important.
1 – Global Imbalances
This represents an enduring feature of the global economic system and while everyone can agree that they need to be resolved some way or the other I think that the proper understanding of demographics shows us that they are essentially structural. Especially on the side of surplus economies I have argued (both in my thesis and in genera) why we cannot suddenly expect economies such as Germany and Japan to do their part and crucially, why we should expect more economies to venture down the same path as they are also ageing rapidly. Importantly, this provides a concrete theoretical spin to the question everyone seems to be asking at the moment of who exactly is going to run the deficits? The pessimistic answer here is no-one and herein lies the rub.
2 – Export dependency
This one is essentially the concrete theoretical proposition used to make the argument above on global imbalances. Ageing leads to a decline in domestic demand and in a closed economy there is really not a lot you can do; savings/investment will fall and consumption will be lacklustre since there is no underlying dynamic to feed it other than dissaving. However, in an open economy you can fight this through claims on other economies or put in another way, you can save more than merited by domestic demand and thus you can invest your savings abroad. Note here that technically this is exactly what e.g. Germany and Japan are doing in the sense that their excess savings have to be matched by excess borrowing/investment demand elsewhere.
I am still developing these two areas, but there are plenty of meat on this topic I think. One crucial task is to develop the life cycle hypothesis on the basis of observed behavior of economies as they age and another is to.
Stay tuned for the next post in this series which looks at the influence from demographics on asset prices, demand, and return and composition of consumption. Suggestions and comments on potential omissions on my part are welcome.
 - Most often operationalized through an OLG framework.
 - Evolutionary Growth goes back to this one "Nelson, R.R., Winter, S.G., 1982. An Evolutionary Theory of Economic Change. Harvard University Press, Cambridge, MA" and is a must read I think. The work by Jan Fagerberg is a good place to begin as well as for a more modern exposition.
 - I.e. demographics and savings and investment behavior in an open vs closed economy